A new global approach, called 'Generalized Ellipsometry', is now capable to characterize the optical and structural properties of general anisotropic layered systems, including absorption, and can be applied, in general, to determine the linear response tensor elements for wavelengths from the far IR to the deep UV. This technique enables new insights into physical phenomena of layered anisotropic mediums, and can provide precise structural and optical data of novel compound materials. Experimental results are presented for stibnite single crystals as example for an arbitrary biaxial absorbing material, a wurtzite GaN thin film with uniaxial anisotropy grown on sapphire, a spontaneously atomically ordered III-V semiconductor alloy thin film, and a sculptured titanium dioxide film with symmetrically dielectric tensor properties.